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In fact, the Black–Scholes formula for the price of a vanilla call option (or put option) can be interpreted by decomposing a call option into an asset-or-nothing call option minus a cash-or-nothing call option, and similarly for a put—the binary options are easier to analyze, and correspond to the two terms in the Black–Scholes formula.
In mathematical finance, the Black–Scholes equation, also called the Black–Scholes–Merton equation, is a partial differential equation (PDE) governing the price evolution of derivatives under the Black–Scholes model. [1]
The Black formula is easily derived from the use of Margrabe's formula, which in turn is a simple, but clever, application of the Black–Scholes formula. The payoff of the call option on the futures contract is (, ()). We can consider this an exchange (Margrabe) option by considering the first asset to be () and the second asset to be riskless ...
The Black-Scholes option-pricing model, first published in 1973 in a paper titled "The Pricing of Options and Corporate Liabilities," was delivered in complete form for publication to
The Black–Scholes formula (hereinafter, "BS Formula") provides an explicit equation for the value of a call option on a non-dividend paying stock. In case the stock pays one or more discrete dividend(s) no closed formula is known, but several approximations can be used, or else the Black–Scholes PDE will have to be solved numerically.
In the Black–Scholes model, the price of the option can be found by the formulas below. [27] In fact, the Black–Scholes formula for the price of a vanilla call option (or put option) can be interpreted by decomposing a call option into an asset-or-nothing call option minus a cash-or-nothing call option, and similarly for a put – the binary options are easier to analyze, and correspond to ...
It can be measured in percentage probability of expiring in the money, which is the forward value of a binary call option with the given strike, and is equal to the auxiliary N(d 2) term in the Black–Scholes formula.
The Black model extends Black-Scholes from equity to options on futures, bond options, swaptions, (i.e. options on swaps), and interest rate cap and floors (effectively options on the interest rate). The final four are numerical methods, usually requiring sophisticated derivatives-software, or a numeric package such as MATLAB.